Related papers: Averaging principles for non-autonomous two-time-s…
Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous…
This article extends a strong averaging principle for L\'evy diffusions which live on the leaves of a foliated manifold subject to small transversal L\'evy type perturbation to the case of non-compact leaves. The main result states that the…
We provide necessary and sufficient first order geometric conditions for the stochastic invariance of a closed subset of R^d with respect to a jump-diffusion under weak regularity assumptions on the coefficients. Our main result extends the…
An averaging principle is derived for the abstract nonlinear evolution equation where the almost periodic right hand-side is a continuous perturbation of the time-dependent family of linear operators determining a linear evolution system.…
We consider parameter estimation of the reaction term for a second order linear parabolic stochastic partial differential equation in two space dimensions driven by a $Q$-Wiener process under small diffusivity. We first construct an…
In this work, we investigate a reaction-diffusion system in which both species are influenced by self-diffusion. Due to Hopf's boundary lemma, we obtain the boundedness of the classical solution of the system. By considering a particular…
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…
In the paper, we consider the no-explosion condition and pathwise uniqueness for SDEs driven by a Poisson random measure with coefficients that are super-linear and non-Lipschitz. We give a comparison theorem in the one-dimensional case…
Generalizing results of \cite{MC,S} and \cite{HSZ} for certain model reaction-diffusion and reaction-convection-diffusion equations, we derive and rigorously justify weakly nonlinear amplitude equations governing general Turing bifurcation…
We consider a class of time-homogeneous diffusion processes on $\mathbb{R}^{n}$ with common invariant measure but varying volatility matrices. In Euclidean space, we show via stochastic control of the diffusion coefficient that the…
A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…
In the study of geometric surface evolutions, stochastic reaction-diffusion equation provides a powerful tool for capturing and simulating complex dynamics. A critical challenge in this area is developing numerical approximations that…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
This work is devoted to averaging principle of a two-time-scale stochastic partial differential equation on a bounded interval $[0, l]$, where both the fast and slow components are directly perturbed by additive noises. Under some regular…
In this paper, we study a very general stochastic variational inequality(SVI) having jumps, random coefficients, delay, and path dependence, in infinite dimensions. Well-posedness in terms of the existence and uniqueness of a solution is…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
In a previous article \cite{kn:anirban1} a method has been introduced to derive the all order Bose-Einstein distribution of the non interacting Bosons as the solution of the Wigner equation. The process was a perturbative one where the…
An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to…